A compass needle deflects in the direction shown in Figure P17.1. Say everything you can about the circuit.

Robert H.

Numerade Educator

You have a lightbulb with a constant current through it. (a) What happens if a compass is placed under the constant current two-wire cable to the bulb? (b) What happens if you separate the wires and

place the compass under one of the separated wires? Explain your answers for both parts.

Robert H.

Numerade Educator

The current through a circuit is shown in Figure P17.3. The deflection of a compass needle is shown in the figure. Is the picture correct? If not, what is wrong?

Robert H.

Numerade Educator

A magnetic field is said to exist in a region of space. Describe three experiments you could do to confirm this statement.

Donald A.

Numerade Educator

three experiments you could do to confirm this statement.

Donald A.

Numerade Educator

In Houston, Earth's $\vec{B}$ field has a magnitude of $5.2 \times 10^{-5} \mathrm{T}$ and points in a direction $57^{\circ}$ below a horizontal line pointing north. Determine the magnitude and direction of the magnetic force exerted by the magnetic field on a 10 -m-long vertical wire carrying a 12 -A current straight upward.

Robert H.

Numerade Educator

$ \mathrm{A} 15-\mathrm{g} 10$ -cm-long wire is suspended horizontally between

the poles of a horseshoe magnet. When the $0.50-\mathrm{A}$ current

in the wire is turned on, the wire jumps up and out of the magnet. What can you learn about the magnet using this information?

Robert H.

Numerade Educator

A metal rod of length $l$ and mass $m$ is suspended in a magnetic field from two light wires that are connected to a battery with emf $\varepsilon$ . When a vertical magnetic field $\vec{B}$ is turned on, the supporting wires make an angle $\theta$ with the vertical. What can you learn about the circuit using this information? Make a list of physical quantities and explain how to determine three of

them.

Donald A.

Numerade Educator

A metal rod is connected to a battery through two stiff metal wires that hold the rod horizontally. The rod is between the poles of a horseshoe magnet that is sitting on a mass-measuring platform scale, which reads 100 g. Draw the magnetic poles of the magnet and the battery connected to the metal

rod so that when you turn the current in the circuit on (a) the reading of the scale supporting the magnet increases; (b) the reading decreases.

Robert H.

Numerade Educator

After you turned on the current in the circuit described

in the previous problem, the scale supporting the magnet

read 106 $\mathrm{g}$ . The rod is 7.0 $\mathrm{cm}$ long and the current through

it is 1.0 $\mathrm{A}$ . What can you learn about the magnet using this

information?

Robert H.

Numerade Educator

Describe a problem for which the following equation is a solution:

$0.70 \mathrm{A}=\frac{3.0 \mathrm{N}}{(0.20 \mathrm{m}) B}$

Robert H.

Numerade Educator

A square coil with 30 turns has sides that are 16 $\mathrm{cm}$ long.

When it is placed in a $0.30-\mathrm{T}$ magnetic field, a maximum

torque of 0.60 $\mathrm{N} \cdot \mathrm{m}$ is exerted on the coil. What can you learn

about the coil from this information?

Robert H.

Numerade Educator

A 5.0 -A current runs through a 10 -turn $(0.12 \mathrm{m})^{2}$ -area

coil. The coil is in a $0.15-$ T magnetic field. What is the direction of the magnetic moment of the coil? Determine the torque exerted on the coil (the magnitude and the direction it tends to turn the coil if initially at rest) for each orientation shown in Figure $P 17.13$ .

Robert H.

Numerade Educator

A 3.0 -A current flows through the wire. (b) Determine

the net torque caused by forces $\vec{F}_{\vec{B}}$ on a and $\vec{F}_{\vec{B}}$ on $c$ and the

torque caused by force $\vec{F}_{\vec{B}}$ on $b$

Donald A.

Numerade Educator

A 500-turn coil of wire is hinged to the top of a table, as

shown in Figure P17.15. Each side of the movable part of

the coil has a length of 0.50 m. (a) In which direction should

a magnetic field point to help lift the free end of the coil off

the table? (b) Determine the torque caused by a 0.70-T field

pointing in the direction described in part (a) when there is a

0.80-A current through the wire and when the coil is parallel

to the table.

Donald A.

Numerade Educator

An electric motor has a square armature with 500 turns. Each side of the coil is 12 cm long and carries a current of 4.0 A. The magnetic field inside the motor is 0.60-T. Choose two orientations of the coil for which you can calculate force-related and torque-related quantities. Draw pictures to show the relative orientations of the coil and the magnetic field vectors.

Donald A.

Numerade Educator

A 20 -turn 5.0 $\mathrm{cm}$ by 5.0 $\mathrm{cm}$ coil hangs with the plane of

the coil parallel to a 0.12 -T magnetic field. (a) Determine the torque on the coil when there is a 0.50 -A current through it. (b) The support for the coil exerts an opposing torque, which

increases as the coil is deflected. The opposing torque is calculated using the equation $\tau=-0.016 \theta$ (in units of $\mathrm{N} \cdot \mathrm{m}$ ), with the angle $\theta$ in units of radians (Figure $\mathrm{P} 17.17 )$ At approximately what angle does the magnetic torque balance the

torque caused by the supporting wire?

Donald A.

Numerade Educator

Electric motor 2 An electric motor has a circular armature with 250

turns of radius 5.0 $\mathrm{cm}$ through which an $8.0-\mathrm{A}$ current flows. The maximum torque exerted on the armature as it turns in a magnetic field is 1.9 $\mathrm{N} \cdot \mathrm{m} .$ Show the orientation of the armature coil in the magnetic field when this torque is exerted on it and determine the magnitude of the field.

Donald A.

Numerade Educator

Each of the lettered dots a-d shown in Figure $P 17.19$ represents a $+1.0 \times 10^{-5}-\mathrm{C}$ charged particle moving at speed $2.0 \times 10^{7} \mathrm{m} / \mathrm{s} .$ A uniform $0.50-\mathrm{T}$ magnetic field points in the positive $z-\mathrm{di}-$

rection. Determine the magnitude of the magnetic force that the field exerts on each particle and indicate carefully, in a drawing, the direction of the force.

Donald A.

Numerade Educator

A duck accumulates a positive charge of 3.0 $\times 10^{-8} \mathrm{C}$ while flying north at speed 18 $\mathrm{m} / \mathrm{s}$ . Earth's magnetic field at the duck's location has a magnitude of

$5.3 \times 10^{-5} \mathrm{T}$ and points in a direction $62^{\circ}$ below a horizontal

line pointing north. Determine the magnitude and direction of the force exerted by Earth's magnetic field on the duck.

Donald A.

Numerade Educator

An electron of mass $9.1 \times 10^{-31} \mathrm{kg}$ moves horizontally toward the north at $3.0 \times 10^{7} \mathrm{m} / \mathrm{s}$ . Determine the magnitude and direction of a $\vec{B}$ field that will exert a magnetic force that balances the gravitational force that Earth exerts on the electron.

Donald A.

Numerade Educator

A 1000 -kg car moves west along the equator. At this location Earth's magnetic field is $3.5 \times 10^{-5} \mathrm{T}$ and points north parallel to Earth's surface. If the car carries a charge of

$-2.0 \times 10^{-3} \mathrm{C},$ how fast must it move so that the magnetic

force balances 0.010$\%$ of Earth's gravitational force exerted on the car?

Donald A.

Numerade Educator

A hydroxide ion $\left(\mathrm{OH}^{-}\right)$ in a glass of water has an aver age speed of about 600 $\mathrm{m} / \mathrm{s}$ . (a) Determine the electrical force between the hydroxide ion (charge $-e )$ and a positive ion (charge $+e )$ that is $1.0 \times 10^{-8} \mathrm{m}$ away (about the separation of 30 atoms). (b) Determine the maximum magnetic force that Earth's $3.0 \times 10^{-5}-\mathrm{T}$ magnetic field can exert on the ion. (c) On the basis of these two calculations, does it seem likely that Earth's magnetic field has much effect on the biochemistry of the body?

Donald A.

Numerade Educator

An alien from a planet in the galaxy M31 (Andromeda) has a ray gun that shoots protons at a speed of $2.0 \times 10^{5} \mathrm{m} / \mathrm{s}$ Design a magnetic shield that will deflect the protons away from your body. Using rough estimates, show that your magnetic shield will, in fact, protect you. Indicate the orientation of your protective device’s magnetic field relative to the direction of the proton

beam and the direction in which the ions are deflected.

Donald A.

Numerade Educator

An electron beam moves toward an oscilloscope screen.

Estimate its vertical displacement caused by Earth’s magnetic

field.

Donald A.

Numerade Educator

An electron and a proton, moving side by side at the same

speed, enter a 0.020-T magnetic field. The electron moves in

a circular path of radius 7.0 mm. Describe the motion of the

proton qualitatively and quantitatively.

Donald A.

Numerade Educator

An east-west electric power line carries a 500 -A current toward

the east. The line is 10 $\mathrm{m}$ above Earth's surface. Determine the

magnitude and direction of the magnetic field at Earth's surface

directly under the wire. What assumptions did you make?

Donald A.

Numerade Educator

A solenoid of radius 1.0 $\mathrm{m}$ with 750 turns and a length of 5.0 $\mathrm{m}$ surrounds a pigeon cage. What current must be in the solenoid so that the solenoid field just cancels

Earth's $4.2 \times 10^{-5}$ - T magnetic field (used occasionally by the pigeons to determine the direction they travel)?

Donald A.

Numerade Educator

wo wires each of length $L$ with current $I$ are placed parallel to each other separated by a distance $d$ . What physical quantities can you determine using this information? How will the

values of these quantities change if one of the currents is reversed? If one of the currents is doubled?

Donald A.

Numerade Educator

A coil of radius $r$ is made of $N$ circular loops. It is connected

to a battery of known emf and internal resistance. The coil produces a magnetic field whose magnitude at the center of the coil is $\vec{B}$ . Make a list of physical quantities you can determine using this information and show how to determine two of them.

Donald A.

Numerade Educator

You have a $9-V$ battery, a set of $1050-\Omega$ resistors, and a long $(2-\mathrm{m})$ connecting wire. Estimate the maximum magnitude of the $\vec{B}$ field that you can produce with this equipment. Make sure you explain how you arrive at your estimate.

Donald A.

Numerade Educator

The equation below describes a process involving magnetism. Solve for the unknown quantity

and draw a sketch that represents a possible process described by the equation.

$$

\begin{array}{l}{\left(1.6 \times 10^{-19} \mathrm{C}\right)\left(2.0 \times 10^{7} \mathrm{m} / \mathrm{s}\right)\left(3.0 \times 10^{-5} \mathrm{T}\right)} \\ {=\left(1.7 \times 10^{-27} \mathrm{kg}\right)\left(2.0 \times 10^{7} \mathrm{m} / \mathrm{s}\right)^{2} / r}\end{array}

$$

Donald A.

Numerade Educator

The equation below describes a process involving magnetism. Solve for the unknown quantity

and draw a sketch that represents a possible process described by the equation.

$$

2 T-(0.020 \mathrm{kg})(9.8 \mathrm{N} / \mathrm{kg})+(10 \mathrm{A})(0.10 \mathrm{m})(0.10 \mathrm{T})=0

$$

Donald A.

Numerade Educator

The equation below describes a process involving magnetism. Solve for the unknown quantity

and draw a sketch that represents a possible process described by the equation.

$$

\begin{array}{l}{100(2.0 \mathrm{A})\left(4.0 \times 10^{-2} \mathrm{m}^{2}\right)(0.20 \mathrm{T})} \\ {-m(9.8 \mathrm{N} / \mathrm{kg})(0.10 \mathrm{m})=0}\end{array}

$$

Donald A.

Numerade Educator

The magnitude of the $\vec{B}$ field inside a solenoid is given by the equation $B=\mu_{0} I(N / L),$ where $N$ is the number of turns and $L$ is the length of the solenoid. (a) Describe an

experiment that can help you test this relation. (b) Explain whether this equation is an operational definition of the magnitude of the $\vec{B}$ field magnitude or a cause-effect relationship. (c) Powerful industrial solenoids produce $\vec{B}$ field magnitudes of about 30 $\mathrm{T}$ . Estimate the relevant physical quantities for such solenoids.

Donald A.

Numerade Educator

In a simplified model of the hydrogen atom, an electron moves with a speed of $1.09 \times 10^{6} \mathrm{m} / \mathrm{s}$ in a circular orbit with a radius of $2.12 \times 10^{-10} \mathrm{m} .$ (a) Determine the time interval for one trip around the circle. (b) Determine the current corresponding to the electron's motion. (c) Determine the magnetic field at the center of the circular orbit and the magnetic moment of the atom.

Donald A.

Numerade Educator

Two long, parallel wires are separated by 2.0 $\mathrm{m}$ . Each wire

has a 30 -A current, but the currents are in opposite directions.

(a) Determine the magnitude of the net magnetic field midway

between the wires. (b) Determine the net magnetic field at a

point 1.0 $\mathrm{m}$ to the side of one wire and 3.0 $\mathrm{m}$ from the other wire.

Donald A.

Numerade Educator

During World War II, explosive mines

were dropped by the Nazis in the harbors of England. The

mines, which lay at the bottom of the harbors, were activated

by the changing magnetic field that occurred when a large

metal ship passed above them. Small English boats called

minesweepers would tow long, current-carrying coils of wire

around the harbors. The field created by the coils activated

the mines, causing them to explode under the coils rather

than under ships. (a) Determine the current that must flow in

one long, straight wire to create a 0.0050-T magnetic field at a

depth of 20 m under the water. The magnetic permeability of

water is about the same as that of air.

Donald A.

Numerade Educator

You have a compass, a $9-\mathrm{V}$ battery, and a 50 - \Omega resistor.

You wish to show your friends how Oersted's experiment works. Will you be able to do this with the available equipment? Explain how you made your decision.

Donald A.

Numerade Educator

A blood flow meter measures a potential difference of $8.0 \times 10^{-5} \mathrm{V}$ across a vessel of diameter $4.0 \times 10^{-3} \mathrm{m}$ . (a) Determine the magnitude of the electric

force exerted on an ion of charge $1.6 \times 10^{-19} \mathrm{C}$ (b) At what

speed must the ion move so that the electric force is balanced

by the magnetic force exerted by a $0.040-\mathrm{T}$ field oriented perpendicular to the flow direction?

Donald A.

Numerade Educator

An electron moves between two parallel plates, as shown

in Figure $\mathbf{P} 17.41 . \mathrm{A} 480-\mathrm{N} / \mathrm{C} \vec{E}$ field points from the upper plate toward the lower plate. A 0.12 -T magnetic field points into the paper. (a) Determine the electric force (magnitude and direction) that the electric field exerts on an electron between the plates. (b) At Figure $P 17.41$ what speed and in which direction (right or left) must the electron move so that the magnetic field exerts an opposing force that balances the electric force? (If narrow slits are placed at the entrance and exit of the plates, the device allows charged particles of only

one speed to pass through both slits. Such a device is called a

velocity selector.)

Donald A.

Numerade Educator

An electron moves at speed $8.0 \times 10^{6} \mathrm{m} / \mathrm{s}$ toward the right

between two parallel plates, such as shown in Figure $\mathrm{P} 17.41 .$

A 0.12 - T magnetic field points into the paper parallel to the

plate surfaces. (a) Determine the magnitude and direction of the magnetic force that the magnetic field exerts on the electron. (b) What should be the magnitude and direction of an $\vec{E}$

field caused by oppositely charged plates to produce an electric force that just balances the magnetic force?

Donald A.

Numerade Educator

Electrons start at rest and pass through a $+28-\mathrm{kV}$ potential difference in an oscilloscope that is oriented so that the electron is moving perpendicular to Earth's $3.5 \times 10^{-5}-\mathrm{T}$ magnetic field at the equator. The oscilloscope faces east. Determine everything you can about the path of the electron.

Donald A.

Numerade Educator

A mass spectrometer has a velocity selector that allows ions traveling at only one speed to pass with

no deflection through slits at the ends. While moving through the velocity selector, the ions pass through $\mathrm{a} 60,000-\mathrm{N} / \mathrm{C}$ $\vec{E}$ field and a $0.0500-\mathrm{T} \vec{B}$ field. The quantities $\vec{v}, \vec{E},$ and $\vec{B}$ are mutually perpendicular. (a) Determine the speed of the ions that are not deflected. (b) After leaving the velocity selector, the ions continue to move in the 0.0500 -T magnetic field. Determine the radius of curvature of a singly charged lithium ion, whose mass is $1.16 \times 10^{-26} \mathrm{kg}$ .

Donald A.

Numerade Educator

One type of mass spectrometer accelerates ions of charge $q,$ mass $m,$ and initial speed zero

through a potential difference $\Delta V .$ The ions then enter a magnetic field where they move in a circular path of radius $r$ . How is the mass of the ions related to these other quantities?

Donald A.

Numerade Educator

An ion with charge $1.6 \times 10^{-19} \mathrm{C}$ moves at speed $1.0 \times 10^{6} \mathrm{m} / \mathrm{s}$ into and perpendicular to the $0.30-\mathrm{T} \mathrm{mag}-$

netic field of a mass spectrometer. After entering the field, the

ion moves in a circular path of radius 0.31 $\mathrm{m} .$ What physical

quantities describing the field and the ion can you determine

using this information? Determine them.

Donald A.

Numerade Educator

A box has either an electric field or a magnetic field inside.

Describe experiments that you might perform to determine

which field is present and its orientation.

Donald A.

Numerade Educator

A wire, shown in Figure P17.48, moves downward perpendicular to a magnetic field.

(a) In what direction will the electrons in the wire move?

(b) After the electrons are forced in one direction, leaving positive charges behind, an $\vec{E}$ field and potential difference $\Delta V$ develop from one end of the wire to the other. The electrons no longer move, since the electric and magnetic forces exerted on them

balance. Show that this happens when the potential difference

from one end of the wire to the other is $\Delta V=v L B$ , where $v$ is

the speed of the wire, $L$ is its length, and $B$ is the magnitude of

the magnetic field. Describe two real-world situations where

this phenomenon might occur.

Donald A.

Numerade Educator

Charge separation on Boeing 747 Determine the potential difference developed across the wings of a Boeing 747 airliner when traveling north at 240 $\mathrm{m} / \mathrm{s}$ . The wingspan is 60 $\mathrm{m}$ . Earth's $5.0 \times 10^{-5}-$ T magnetic field points in a direction $60^{\circ}$ below a

horizontal line directed north. In solving this problem, follow the outline developed in the previous problem. Note that the magnetic field is not perpendicular to the plane's velocity.

Donald A.

Numerade Educator

Particles in cosmic rays are mostly protons, which have energies up to about $10^{20} \mathrm{eV},$ where 1 $\mathrm{eV}$ is the change in the kinetic energy of an electron moving through a potential

difference of 1 V. Use this information to estimate the path of these particles in Earth’s atmosphere. State the assumptions that you are making in your estimate.

Donald A.

Numerade Educator

The solenoid magnetic field in an MRI apparatus is greater than Earth's $5.0 \times 10^{-5}$ T magnetic field by about how many times?

(a) 40

(b) 400

(c) 4000

(d) $40,000$

(e) $400,000$

Donald A.

Numerade Educator

The energy of the probe field causes protons to flip when in a

1.50000 -T magnetic field. $A \pm 0.001-$ T variation in the magnetic field causes a mismatch with the radio frequency flipping field and no flipping at a distance of 0.002 $\mathrm{m}$ from where the magnetic field is matched to the flipping field. Which answer below is closest to the change in the $B$ field per unit distance?

(a) 0.08 $\mathrm{T} / \mathrm{m}$

(b) 0.8 $\mathrm{T} / \mathrm{m}$

(c) 8 $\mathrm{T} / \mathrm{m}$

(d) 0.003 $\mathrm{T} \cdot \mathrm{m}$

(e) 0.000003 $\mathrm{T} / \mathrm{m}$

Donald A.

Numerade Educator

Using your answer to Problem 52, determine the quantity closest to the amount that the auxiliary magnetic field causes the magnetic field to vary over a 0.20-m region of the body being mapped by MRI.

$\begin{array}{llll}{\text { (a) } 4 \mathrm{T}} & {\text { (b) } 2 \mathrm{T}} & {\text { (c) } 0.002 \mathrm{T}} & {\text { (d) } 0.02 \mathrm{T}} & {\text { (e) } 0.2 \mathrm{T}}\end{array}$

Donald A.

Numerade Educator

The MRI apparatus is able to look at proton concentration (and hence hydrogen concentration) at one tiny part of the body by doing what?

(a) Aiming the probe field at the whole body

(b) Varying the probe field frequency so that only protons in

one place are flipped

(c) Varying the $B$ field over the body so $\Delta U=2 \mu B$ matches

the probe field energy at one small location

(d) Placing a small hole in a body shield so the probe field

reaches only one part of body

(e) All of the above

Donald A.

Numerade Educator

Which answer below is closest to the energy of the probe field needed to flip protons? The magnetic dipole moment of a proton is $1.41 \times 10^{-26} \mathrm{J} / \mathrm{T} .$

(a) 4 $\mathrm{J}$

(b) $4 \times 10^{-10} \mathrm{J}$

(c) $4 \times 10^{-25} \mathrm{J}$

(d) $4 \times 10^{-26} \mathrm{J}$

(e) $4 \times 10^{-27} \mathrm{J}$

Donald A.

Numerade Educator

Why might a herniated disk projecting slightly out from between two vertebrae look different in an MRI image than a nonherniated disk?

(a) The vertebrae adjacent to a herniated disk are closer than vertebrae beside a nonherniated disk.

(b) There is a different concentration of hydrogen atoms in bone and in disks.

(c) Protons in the herniation produce an image that can be seen.

(d) b and c

(e) a, b, and c

Donald A.

Numerade Educator

Which answer below is closest to the ratio of the power line $\vec{B}$ field on the ground 50 $\mathrm{m}$ below a 100 -A current and Earth's $\vec{B}$ field at the same location?

$\begin{array}{llll}{\text { (a) } 0.001} & {\text { (b) } 0.01} & {\text { (c) } 0.1} & {\text { (d) } 10} & {\text { (e) } 100}\end{array}$

Donald A.

Numerade Educator

A $550-\mathrm{W}$ toaster oven is connected to a $110-\mathrm{V}$ wall outlet.

Which answer below is closest to the electric current in one of

the wires from the wall outlet to the oven?

(a) 0.2 $\mathrm{A}$

(b) $50,000 \mathrm{A}$

$(\mathrm{c}) \quad 1 \mathrm{A}$

(d) 5 $\mathrm{A}$

(e) 20 $\mathrm{A}$

Donald A.

Numerade Educator

Which answer below is closest to the ratio of the magnetic

field produced 0.4 m from the cable for the toaster oven in the

last problem and Earth’s magnetic field? (This is assuming the

current flows in only one direction—which it does not.)

(a) 0.001 (b) 0.003 (c) 0.05 (d) 0.5 (e) 5

Donald A.

Numerade Educator

Leukemia rates have declined in recent years, whereas the magnitudes of the $\vec{B}$ fields created by power lines in our environment have increased significantly. Why does this not necessarily rule out power line magnetic fields as a contributing cause of leukemia?

(a) Correlation studies have no cause-effect relationship.

(b) There is no known mechanism for power line magnetic field-induced deaths.

(c) The power line magnetic fields cannot penetrate clothing and skin.

(d) Perhaps the power line magnetic field-induced cancers have increased from 0.001 to 0.025 of the cases and other causes have decreased.

(e) a, b, and d

(f) All of the above

Donald A.

Numerade Educator

Why would scientists be concerned about the relationship between magnetic fields and human health but not so much about electric fields and human health?

(a) The human body is a conductor.

(b) Many molecules are dipoles.

(c) There are moving electrically charged particles inside the body.

(d) Magnetic fields are more dangerous than electric fields.

(e) Electric fields are reflected from clothing but magnetic fields are not.

Donald A.

Numerade Educator

The 1979 epidemiologic study is a(n)

(a) testing experiment.

(b) observational experiment.

(c) hypothesis and a testing experiment.

(d) observational experiment and a hypothesis.

Donald A.

Numerade Educator

The mice experiment in the study of the effects of magnetic fields on health is a(n)

(a) observational experiment. (b) testing experiment.

(c) assumption. (d) proof.

Donald A.

Numerade Educator

Draw $\vec{B}$ field lines for the magnetic field produced by the objects shown in Figure

$\mathbf{P} 17.4 .$

Check back soon!